Geological materials are inherently discontinuous because of joints, faults, shears, bedding, and foliation planes which typically transect the rock mass. Over the past two decades enormous effort has been made by the rock mechanics community to quantify the characterization of rock structure by developing better geo-statistical tools and by developing more general constitutive laws for the mechanical strength of discontinuities. Along with these developments a substantial effort has been made to develop better and more suitable numerical methods, which allow realistic modelling of discontinuous deformation in geological materials. In particular, the discrete element method (DEM), the combined discrete-finite element methods (FEM/DEM), and discontinuous deformation analysis (DDA) have reached a mature development stage. In this book 24 high quality, peer-reviewed papers on discontinuous analysis in geological materials, written by leading experts from 17 countries, are presented in six chapters:1) Key note lecture, 2) Plenary lectures, 3) Case studies in rock slope and underground openings in discontinuous rock, 4) Analysis, response, prediction, and monitoring of existing rock and stone monuments, 5) Validation of theoretical models, 6) Theoretical developments in modelling discontinuous deformation. It is believed that the collection of papers in this volume demonstrates the directions in which theoretical developments in analysis of discontinuous deformation should proceed, the validity and limitations of existing codes, and the range of engineering problems to which discontinuous analysis can be applied.